A solid circular shaft transmits 10 kW at 1440 rpm. Material shear yield stress is 150 MPa and safety factor 2. Find static-strength diameter in mm to two decimals.
Allowable shear is 150/2 = 75 MPa. Torque is $T=P/\omega=10000/[2\pi(1440/60)]=66.3146$ N·m. Using $\tau_{max}=16T/(\pi d^3)$ with T = 66314.6 N·mm gives $d=[16(66314.6)/(75\pi)]^{1/3}=\mathbf{16.51}$ mm.
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